You look at a carnival game. The person running it says, "Just reach your hand into this bag. There are 9 yellow balls and 1 red ball in the bag. You get 4 chances to pull out the red ball. (You have to put the ball you drew back before you draw another ball.) You only have to pay one dollar to play, and you get 3 dollars if you pull out the red ball!"

Assuming the person running the game is telling the truth, and the balls only differ in color, would you expect to make a net profit or a net loss on this game?

From my limited understanding of probability calculations the way to approach this is by calculating the chance of failure. The only way to fail is by picking 4 consecutive yellows, so

P(fail) = 0.9^4 = 0.6561

which means that.

P(win) = 1 - P(fail) = 0.3439

The cost of failing is $1, the benefit of winning is $2 ($3 winnings minus $1 to play).

So the net gain/loss is:

Gain/loss = P(win)x2 - P(fail)x1 = 0.3439x2 - 0.6561 = 0.0309

This is positive, which implies I should expect a net gain if I play for long enough.

However, it's a game at a carnival therefore I would expect to make a net loss irrespective of what the probabilities may show! My guess is that either I've missed the trick somewhere or my knowledge of probability calculations is even worse than I thought.

Posted by fwaff on 2003-09-18 08:18:31